Course materials for 2021-11-9 AFEC at XTBG.
Did you install picante and FD?
install.packages("picante")
install.packages("FD")It’s better if you have those packages too.
install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")Load packages.
library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)samp <- read_csv("./data/samp.csv")
DT::datatable(samp)samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Site
samp_mat## Illicium_macranthum Manglietia_insignis Michelia_floribunda
## Site1 1 0 0
## Site2 1 2 2
## Site3 1 0 0
## Site4 1 1 0
## Site5 1 0 0
## Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii
## Site1 0 0 0
## Site2 2 0 0
## Site3 0 0 2
## Site4 0 0 2
## Site5 0 1 1
## Actinodaphne_forrestii Machilus_yunnanensis
## Site1 0 0
## Site2 0 0
## Site3 2 2
## Site4 2 0
## Site5 0 0
phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait <- read_csv("./data/dummy_trait.csv")
# trait <- read.csv("./data/dummy_trait.csv") is fine too.
DT::datatable(trait)trait_long <- trait |>
pivot_longer(LMA:SM, names_to = "trait")
trait_long## # A tibble: 616 × 3
## sp trait value
## <chr> <chr> <dbl>
## 1 Acer_campbellii LMA 39.8
## 2 Acer_campbellii LL 7.08
## 3 Acer_campbellii Amass 985.
## 4 Acer_campbellii Rmass 54.7
## 5 Acer_campbellii Nmass 6.56
## 6 Acer_campbellii Pmass 0.42
## 7 Acer_campbellii WD 0.46
## 8 Acer_campbellii SM 0.39
## 9 Actinodaphne_forrestii LMA 69.2
## 10 Actinodaphne_forrestii LL 12.5
## # … with 606 more rows
ggplot(trait_long, aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait |>
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) |>
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 |>
pivot_longer(logLMA:logSM, names_to = "trait") |>
ggplot(aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")Skip
res_mds <- metaMDS(samp_mat)## Run 0 stress 0
## Run 1 stress 0.2297529
## Run 2 stress 0.09680996
## Run 3 stress 0.1302441
## Run 4 stress 0.1302441
## Run 5 stress 0.1302441
## Run 6 stress 7.637639e-05
## ... Procrustes: rmse 0.1222676 max resid 0.1833355
## Run 7 stress 0
## ... Procrustes: rmse 0.03078506 max resid 0.05024731
## Run 8 stress 7.277062e-05
## ... Procrustes: rmse 0.1288717 max resid 0.1986277
## Run 9 stress 6.424802e-05
## ... Procrustes: rmse 0.1188153 max resid 0.1762601
## Run 10 stress 0.09680968
## Run 11 stress 0
## ... Procrustes: rmse 0.04420653 max resid 0.05956871
## Run 12 stress 0.09680993
## Run 13 stress 8.666761e-05
## ... Procrustes: rmse 0.04860053 max resid 0.07265191
## Run 14 stress 0
## ... Procrustes: rmse 0.07191474 max resid 0.1097125
## Run 15 stress 0
## ... Procrustes: rmse 0.1046624 max resid 0.1901878
## Run 16 stress 0.1302441
## Run 17 stress 0
## ... Procrustes: rmse 0.04244088 max resid 0.05637964
## Run 18 stress 0
## ... Procrustes: rmse 0.06856883 max resid 0.1191612
## Run 19 stress 0
## ... Procrustes: rmse 0.1089741 max resid 0.1938099
## Run 20 stress 8.598926e-05
## ... Procrustes: rmse 0.1288655 max resid 0.1986309
## *** No convergence -- monoMDS stopping criteria:
## 12: stress < smin
## 2: stress ratio > sratmax
## 6: scale factor of the gradient < sfgrmin
plot(res_mds)We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sense.
ordiplot(res_mds, type = "n")
orditorp(res_mds, display = "species", col = "red", air = 0.01)
orditorp(res_mds, display = "sites", cex = 1.25, air = 0.01)res_pd <- pd(samp_mat, phylo)
res_pd## PD SR
## Site1 1.000000 1
## Site2 3.022727 4
## Site3 2.909091 4
## Site4 3.136364 4
## Site5 2.454545 3
You can always see the help.
?pdcophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
cophenetic(phylo)[1:5, 1:5]## Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii 0.0000000 0.18181818 0.18181818
## Melia_toosendan 0.1818182 0.00000000 0.09090909
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455
## Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.3636364 0.5454545
## Melia_toosendan 0.3636364 0.5454545
## Skimmia_arborescens 0.3636364 0.5454545
## Rhus_sylvestris 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.0000000
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
res_mpd <- mpd(samp_mat, cophenetic(phylo))
res_mpd## [1] NA 1.568182 1.454545 1.606061 1.636364
The above vector shows MPD for each site.
\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.
res_mntd <- mntd(samp_mat, cophenetic(phylo))
res_mntd## [1] NA 1.181818 1.181818 1.295455 1.272727
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
tmp <- trait2 |>
filter(sp %in% colnames(samp_mat))
tmp## # A tibble: 8 × 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_f… 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_… 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macra… 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomso… 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunna… 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_ins… 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_flori… 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71
(ab <- apply(samp_mat, 1, sum))## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3
# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.4121097 -1.832581 0.48
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93
## Site5 14.713415 11.128090 12.759265 5.116104 0.2203436 -6.565585 1.52
## logSM
## Site1 0.3001046
## Site2 0.3114643
## Site3 -1.9909259
## Site4 2.2087792
## Site5 0.3257723
(CWM <- CWS / ab)## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667
## logSM
## Site1 0.3001046
## Site2 0.0444949
## Site3 -0.2844180
## Site4 0.3681299
## Site5 0.1085908
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$spLet’s see a subset of the trait matrix
trait_mat0[1:5, 1:5]## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037
Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])par(mfrow = c(1, 1))Now we can make a trait distance matirx.
trait_dm <- as.matrix(dist(trait_mat))Let’s see the first 5 species.
trait_dm[1:5, 1:5]## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii 0.000000 3.799360 5.216902
## Actinodaphne_forrestii 3.799360 0.000000 2.415031
## Alnus_nepalensis 5.216902 2.415031 0.000000
## Anneslea_fragrans 3.175911 2.335392 3.225141
## Beilschmiedia_robusta 2.545269 2.565063 3.638183
## Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 3.175911 2.545269
## Actinodaphne_forrestii 2.335392 2.565063
## Alnus_nepalensis 3.225141 3.638183
## Anneslea_fragrans 0.000000 1.579930
## Beilschmiedia_robusta 1.579930 0.000000
mpd(samp_mat, trait_dm)## [1] NA 4.288349 3.530805 3.961248 3.438008
ses.mpd(samp_mat, trait_dm)## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z
## Site1 1 NA NaN NA NA NA
## Site2 4 4.288349 3.699333 0.7997150 773 0.7365330
## Site3 4 3.530805 3.739246 0.8216983 433 -0.2536714
## Site4 4 3.961248 3.719409 0.8146425 647 0.2968651
## Site5 3 3.438008 3.753822 1.0090415 422 -0.3129839
## mpd.obs.p runs
## Site1 NA 999
## Site2 0.773 999
## Site3 0.433 999
## Site4 0.647 999
## Site5 0.422 999
mntd(samp_mat, trait_dm)## [1] NA 2.504352 2.697074 1.873825 2.613585
We will make a functional dendrogram using clustring methods. We use UPGMA in this example.
t_clust <- hclust(dist(trait_mat), method = "average")
plot(t_clust)res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.
res_fd## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974
## WD logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691 0.1665816
## Site3 0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.9701997
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.1.2 (2021-11-01)
## os macOS Big Sur 11.6
## system aarch64, darwin20.6.0
## ui unknown
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Asia/Shanghai
## date 2021-11-09
##
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## vctrs 0.3.8 2021-04-29 [1] CRAN (R 4.1.0)
## vegan * 2.5-7 2020-11-28 [1] CRAN (R 4.1.0)
## vroom 1.5.4 2021-08-05 [1] CRAN (R 4.1.1)
## withr 2.4.2 2021-04-18 [1] CRAN (R 4.1.0)
## xfun 0.24 2021-06-15 [1] CRAN (R 4.1.0)
## xml2 1.3.2 2020-04-23 [1] CRAN (R 4.1.0)
## yaml 2.2.1 2020-02-01 [1] CRAN (R 4.1.0)
##
## [1] /opt/homebrew/lib/R/4.1/site-library
## [2] /opt/homebrew/Cellar/r/4.1.2/lib/R/library